Optimal Boundary Control of a Simplified Ericksen-Leslie System for Nematic Liquid Crystal Flows in 2D
Optimal Boundary Control of a Simplified Ericksen-Leslie System for Nematic Liquid Crystal Flows in 2D
复制标题
二维向列液晶流的简化 Ericksen-Leslie 系统的最优边界控制
DOI：
10.1007/s00205-017-1095-2
复制
发表时间：
2017
影响因子：
2.5
通讯作者：
Wu Hao
中科院分区：
文献类型：
--
作者：
Cavaterra Cecilia;Rocca Elisabetta;Wu Hao
In this paper, we investigate an optimal boundary control problem for a two dimensional simplified Ericksen–Leslie system modelling the incompressible nematic liquid crystal flows. The hydrodynamic system consists of the Navier–Stokes equations for the fluid velocity coupled with a convective Ginzburg–Landau type equation for the averaged molecular orientation. The fluid velocity is assumed to satisfy a no-slip boundary condition, while the molecular orientation is subject to a time-dependent Dirichlet boundary condition that corresponds to the strong anchoring condition for liquid crystals. We first establish the existence of optimal boundary controls. Then we show that the control-to-state operator is Fréchet differentiable between appropriate Banach spaces and derive first-order necessary optimality conditions in terms of a variational inequality involving the adjoint state variables.
